Question

Evaluate

x^2y^3 + x(

1 + y^2)dy/dx= 0

Answer 1

$$x^2y^3+x(1+y^2)\dfrac{dy}{dx}=0$$

$x=0, y\in\R$

$y=0, x\in \R$

$xy\not=0$

$$\dfrac{1+y^2}{y^3}dy=-xdx$$

$$\int \dfrac{1+y^2}{y^3}dy=-\int xdx$$

$$-\dfrac{1}{y^2}+\ln|y|=-\dfrac{1}{2}x^2+C$$

$$-\dfrac{1}{y^2}+\ln|y|+\dfrac{1}{2}x^2=C$$